2002 cavalier auto trans shifting hard and the trac light is but it shifted hard after the light came on?

If the PCM (Powertrain Control Module) sees something it doesn't like, it stores the error in it's memory. These are called fault codes or DTCs (Diagnostic Trouble Code). GM designed the software to run in a default mode if a potentially serious problem is seen by the computer. In default mode, the computer commands maximum oil pressure in the transmission. Under a high oil pressure condition in the transmission, the driver may notice harsh shifts as well has harsh engagements into Drive and Reverse.

One of the more common codes that will result in a default conditions is the P1811 code which is "Long shift, maximum adapts". Any problem that results in a default condition should be addressed promptly. Take the vehicle to a transmission specialty shop and have them perform a diagnostic routine on the vehicle.